Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (c, y), endpoint (m, q)
A) $\left( \frac { \mathrm { c } + \mathrm { m } } { 2 } , \frac { \mathrm { y } + \mathrm { q } } { 2 } \right)$
B) $( 2 m - c , 2 q - y )$
C) $( c - m , y - q )$
D) $( 2 c - m , 2 y - q )$

Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (c, y), endpoint (m, q) 
A) $\left( \frac { \mathrm { c } + \mathrm { m } } { 2 } , \frac { \mathrm { y } + \mathrm { q } } { 2 } \right)$
B) $( 2 m - c , 2 q - y )$
C) $( c - m , y - q )$
D) $( 2 c - m , 2 y - q )$

Quizplus · Accepted Answer

The formula for the other endpoint, given the midpoint and one endpoint, is derived from the midpoint formula: $(x_1 + x_2)/2 = c$ and $(y_1 + y_2)/2 = y$. Solving for $x_2$ and $y_2$, we get $x_2 = 2c - m$ and $y_2 = 2y - q$.

Find the Coordinates of the Other Endpoint of the Segment (c+m2,y+q2)\left( \frac { \mathrm { c } + \mathrm { m } } { 2 } , \frac { \mathrm { y } + \mathrm { q } } { 2 } \right)(2c+m​,2y+q​)

Find the Coordinates of the Other Endpoint of the Segment $\left( \frac { \mathrm { c } + \mathrm { m } } { 2 } , \frac { \mathrm { y } + \mathrm { q } } { 2 } \right)$